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A060086 Convolution triangle A059594 with extra first column. 4
1, 0, 1, 0, 1, 1, 0, 2, 2, 1, 0, 2, 5, 3, 1, 0, 3, 8, 9, 4, 1, 0, 3, 14, 19, 14, 5, 1, 0, 4, 20, 39, 36, 20, 6, 1, 0, 4, 30, 69, 85, 60, 27, 7, 1, 0, 5, 40, 119, 176, 160, 92, 35, 8, 1, 0, 5, 55, 189, 344, 376, 273, 133, 44, 9 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

COMMENTS

Riordan array (1, x/((1+x)*(1-x)^2)). - Philippe Deléham, Feb 24 2012

Triangle, read by rows, given by (0, 1, 1, -2, 1/2, 1/2, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. - Philippe Deléham, Feb 24 2012

LINKS

Table of n, a(n) for n=0..64.

FORMULA

G.f.for column m >= 0: (x/((1-x^2)*(1-x)))^m.

T(n,k) = T(n-1,k-1) + T(n-1,k) + T(n-2,k) - T(n-3,k) with T(n,0) = 0^n. - Philippe Deléham, Feb 24 2012

G.f.: (1-x-x^2+x^3)/(1-x-x^2+x^3-y*x). - Philippe Deléham, Feb 24 2012

Sum_{k, 0<=k<=n} T(n,k)*2^k = A181301(n). - Philippe Deléham, Feb 24 2012

EXAMPLE

{1}; {0,1}; {0,1,1}; {0,2,2,1}; ...

Triangle begins :

1

0, 1

0, 1, 1

0, 2, 2, 1

0, 2, 5, 3, 1

0, 3, 8, 9, 4, 1

0, 3, 14, 19, 14, 5, 1

MATHEMATICA

t[0, 0] = 1; t[_, 0] = 0; t[n_, m_] := Sum[ Sum[ Binomial[j, 2*j-3*k-m+n]*(-1)^(j-k)*Binomial[k, j], {j, 0, k}]*Binomial[m+k-1, m-1], {k, 0, n-m}]; Table[t[n, m], {n, 0, 10}, {m, 0, n}] // Flatten (* Jean-François Alcover, Jun 21 2013 *)

CROSSREFS

Cf. A059594,

Sequence in context: A092869 A029337 A280817 * A177975 A062135 A190182

Adjacent sequences:  A060083 A060084 A060085 * A060087 A060088 A060089

KEYWORD

nonn,easy,tabl

AUTHOR

Wolfdieter Lang, Apr 06 2001

STATUS

approved

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Last modified June 16 14:56 EDT 2019. Contains 324152 sequences. (Running on oeis4.)